


def 							UpperCamelCase_( lowerCamelCase_					)       ->		bool:





    if not isinstance(__snake_case				,					__snake_case					):
        raise ValueError('Input series is not valid, valid series - [2, 4, 6]'					)
    if len(__snake_case					) == 0:
        raise ValueError('Input list must be a non empty list'					)
    if len(__snake_case					) == 1:
        return True
    _lowercase			:				str 						=						series[1] - series[0]
    for index in range(len(__snake_case					) - 1					):
        if series[index + 1] - series[index] != common_diff:
            return False
    return True



def 							UpperCamelCase_( lowerCamelCase_					)       ->		float:





    if not isinstance(__snake_case				,					__snake_case					):
        raise ValueError('Input series is not valid, valid series - [2, 4, 6]'					)
    if len(__snake_case					) == 0:
        raise ValueError('Input list must be a non empty list'					)
    _lowercase			:				List[Any] 						=						0
    for val in series:
        answer += val
    return answer / len(__snake_case					)


if __name__ == "__main__":
 import doctest

 doctest.testmod()










"""simple docstring"""
def 							A						(				__snake_case: int = 1_0_0_0_0_0_0  )    ->		int:

       """simple docstring"""





       __magic_name__      				=    limit + 1
       __magic_name__      				=    [0] * limit
       for first_term in range(1 ,     __snake_case  ):
              for n in range(__snake_case ,     __snake_case ,     __snake_case  ):
                     __magic_name__      				=    first_term + n / first_term
                     if common_difference % 4:  # d must be divisble by 4
                            continue
                     else:
                            common_difference /= 4
                            if (
                                first_term > common_difference
                                and first_term < 4 * common_difference
                            ):  # since x,y,z are positive integers
                                   frequency[n] += 1  # so z>0 and a>d ,also 4d<a

       __magic_name__      				=    sum(1 for x in frequency[1:limit] if x == 1_0  )

       return count


if __name__ == "__main__":
 print(f"""{solution() = }""")